Method, device, equipment and medium for determining helical gear meshing stiffness

Abstract

The present invention relates to the technical field of gear mechanics calculation, and particularly relates to a method, device, equipment and medium for determining the meshing stiffness of helical gears, including: analyzing the meshing process based on design and working condition parameters to obtain the initial meshing stiffness; performing dynamic analysis based on the initial meshing stiffness to obtain the dynamic response; discretizing the helical gear pair to determine the load angle of the sliced helical gear; analyzing the meshing condition of the sliced meshing under tooth surface friction in combination with the dynamic response and the load angle to obtain the sliced meshing stiffness; determining the load distribution information of each slice and each contact line based on the meshing stiffness of the sliced helical gear pair and the initial load distribution information to obtain the corrected meshing stiffness; judging convergence according to the corrected meshing stiffness and the initial meshing stiffness, and if not satisfied, iterating to make the iteration result gradually converge on the basis of considering the interaction between the dynamic meshing force and friction, approaching the true performance of the helical gear transmission system, so as to provide an accurate basis for determining the meshing stiffness of helical gears.

Description

Technical Field

[0001] The present invention relates to the technical field of gear mechanics calculation, and particularly to a method, device, equipment and medium for determining the meshing stiffness of helical gears. Background Art

[0002] In the field of mechanical transmission, helical gear transmission systems are widely used due to their advantages such as strong load-bearing capacity and smooth transmission. Previous studies have shown that conducting dynamic modeling research on gear transmission systems can provide a theoretical reference for gear transmission vibration analysis and optimization design. Generally, internal excitations such as gear pair stiffness excitation are important reasons for the vibration and noise of gear transmission systems. Therefore, studying the meshing stiffness and dynamic characteristics of helical gear transmission has important engineering value and scientific significance for the vibration control of helical gear transmission, etc.

[0003] However, there are certain limitations in existing research. Existing helical gear meshing stiffness calculation models generally have problems such as single modeling dimension and incomplete parameter coupling relationships, ignoring the influence of tooth surface friction on the meshing process of helical gears, resulting in a large deviation between the obtained meshing stiffness and the actual situation, which severely restricts the applicable range and calculation accuracy of the model.

[0004] It can be seen that the existing technology still needs to be improved. Summary of the Invention

[0005] In order to overcome the deficiencies of the prior art, the purpose of the present invention is to provide a method, device, equipment and storage medium for determining the meshing stiffness of helical gears, which conducts dynamic analysis of helical gear transmission on the basis of considering the coupling effect between tooth surface friction and helical gears, and improves the analysis accuracy of helical gear transmission systems.

[0006] The first aspect of the present invention provides a method for determining the meshing stiffness of a helical gear, including: analyzing the meshing process of the helical gear based on the obtained design parameters and operating conditions of the helical gear to obtain the initial meshing stiffness; performing dynamic analysis of the helical gear transmission based on the initial meshing stiffness to obtain the dynamic response; discretizing the helical gear pair and determining the meshing point coordinate information of each sliced helical gear obtained by the discretization process, and confirming the load angle of each sliced helical gear based on the meshing point coordinate information; analyzing the meshing situation of the sliced helical gear under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle to obtain the meshing stiffness of the sliced helical gear pair; determining the load distribution information of each slice and each contact line based on the meshing stiffness of the sliced helical gear pair, and obtaining the corrected meshing stiffness based on the load distribution information and the meshing stiffness of the sliced helical gear pair; judging whether the preset convergence condition is satisfied based on the corrected meshing stiffness and the initial meshing stiffness to obtain the convergence judgment result; if the convergence judgment result is that the convergence condition is satisfied, then judging whether the preset iteration stop condition is satisfied, if not, then using the corrected meshing stiffness as the initial meshing stiffness, and returning to perform the dynamic analysis of the helical gear transmission based on the initial meshing stiffness.

[0007] Optionally, in the first implementation manner of the first aspect of the present invention, the performing dynamic analysis of the helical gear transmission based on the initial meshing stiffness to obtain the dynamic response includes: constructing a dynamic model of the helical gear transmission; introducing the initial meshing stiffness into the dynamic model of the helical gear transmission to obtain a dynamic equation set of the helical gear transmission; and solving the dynamic equation set of the helical gear transmission to obtain the initial dynamic response.

[0008] Optionally, in the second implementation manner of the first aspect of the present invention, the discretizing the helical gear pair and determining the meshing point coordinate information of each sliced helical gear obtained by the discretization process, and confirming the load angle of each sliced helical gear based on the meshing point coordinate information includes: discretizing the helical gear pair in the tooth width direction to obtain a plurality of sliced helical gears; constructing a local coordinate system to determine the meshing position of each sliced helical gear pair obtained by the discretization process; and analyzing the force direction of the helical gear pair based on the meshing position of each sliced helical gear to obtain the load angle of each sliced helical gear.

[0009] Optionally, in the third implementation manner of the first aspect of the present invention, the analyzing the meshing situation of the sliced helical gear under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle to obtain the meshing stiffness of the sliced helical gear pair includes: analyzing the force situation of the sliced helical gear under tooth surface friction based on the preset initial load distribution information and dynamic response to obtain the friction force and meshing force of each sliced helical gear; and analyzing the meshing situation of the sliced helical gear based on the load angle, friction force, and meshing force of each sliced helical gear to obtain the meshing stiffness of the sliced helical gear pair.

[0010] Optionally, in the fourth implementation manner of the first aspect of the present invention, determining the load distribution information of each slice and each contact line based on the meshing stiffness of the sliced helical gear pair and the initial load distribution information to obtain the modified meshing stiffness includes: determining the load distribution information of each slice and each contact line based on the meshing stiffness of the sliced helical gear pair and the initial load distribution information to obtain the contact line load distribution information and the meshing stiffness of the contact line helical gear pair; performing superposition calculation on the meshing stiffness of the contact line helical gear pair based on the contact line load distribution information to obtain the modified meshing stiffness.

[0011] Optionally, in the fifth implementation manner of the first aspect of the present invention, after determining whether the preset convergence condition is satisfied based on the modified meshing stiffness and the initial meshing stiffness to obtain the convergence judgment result, it further includes: if the convergence judgment result is that the convergence condition is not satisfied, using the load distribution information as the preset initial load distribution information, and returning to execute the meshing condition analysis of the sliced helical gear under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle.

[0012] Optionally, in the sixth implementation manner of the first aspect of the present invention, if the convergence judgment result is that the convergence condition is satisfied, then it is judged whether the preset iteration stop condition is satisfied. If not, using the modified meshing stiffness as the initial meshing stiffness, and returning to execute the dynamic analysis of helical gear transmission based on the initial meshing stiffness, including: if the current iteration time < the preset maximum iteration time, the preset iteration stop condition is not satisfied; using the modified meshing stiffness as the initial meshing stiffness, and returning to execute the dynamic analysis of helical gear transmission based on the initial meshing stiffness.

[0013] The second aspect of the present invention provides a device for determining the meshing stiffness of a helical gear, including:

[0014] An initialization module, configured to analyze the meshing process of the helical gear based on the obtained design parameters and working condition parameters of the helical gear to obtain the initial meshing stiffness;

[0015] A transmission analysis module, configured to perform dynamic analysis of helical gear transmission based on the initial meshing stiffness to obtain a dynamic response;

[0016] A discretization module, configured to perform discretization processing on the helical gear pair, determine the meshing point coordinate information of each sliced helical gear obtained by the discretization processing, and confirm the load angle of each sliced helical gear based on the meshing point coordinate information;

[0017] A first calculation module, configured to analyze the meshing condition of the sliced helical gear under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle to obtain the meshing stiffness of the sliced helical gear pair;

[0018] A second calculation module, configured to determine the load distribution information of each slice and each contact line based on the meshing stiffness of the sliced helical gear pair and the initial load distribution information, so as to obtain the corrected meshing stiffness;

[0019] A judgment module, configured to judge whether a preset convergence condition is satisfied based on the corrected meshing stiffness and the initial meshing stiffness, so as to obtain a convergence judgment result;

[0020] An iteration module, configured to, if the convergence judgment result is that the convergence condition is satisfied, judge whether a preset iteration stop condition is satisfied; if not, use the corrected meshing stiffness as the initial meshing stiffness, and return to perform the dynamic analysis of the helical gear transmission based on the initial meshing stiffness.

[0021] A third aspect of the present invention provides a device for determining the meshing stiffness of a helical gear. The device for determining the meshing stiffness of a helical gear includes: a memory and at least one processor, wherein instructions are stored in the memory; at least one of the processors calls the instructions in the memory, so that the device for determining the meshing stiffness of a helical gear executes each step of the method for determining the meshing stiffness of a helical gear described in any one of the above.

[0022] A fourth aspect of the present invention provides a computer-readable storage medium, on which instructions are stored, and when the instructions are executed by a processor, each step of the method for determining the meshing stiffness of a helical gear described in any one of the above is implemented.

[0023] In the technical solution of the present invention, the initial meshing stiffness is obtained by analyzing the meshing process based on the design parameters and working condition parameters of the helical gear, and then the meshing stiffness of the helical gear is determined based on the initial meshing stiffness to obtain the initial dynamic response. Using the initial dynamic response as a basis, the meshing process of the spur gear under tooth surface friction is analyzed, and the closed-loop iteration of "stiffness calculation - load distribution - stiffness correction" is realized through an iterative algorithm, so that the model gradually converges on the basis of considering the interaction between dynamic meshing force and friction, approaching the true performance of the helical gear transmission system, thereby providing a basis for determining the meshing stiffness of the helical gear. Description of the Drawings

[0024] Figure 1 It is a logic flow chart of the method for determining the meshing stiffness of a helical gear provided by an embodiment of the present invention;

[0025] Figure 2 It is a structural schematic diagram of the device for determining the meshing stiffness of a helical gear provided by an embodiment of the present invention;

[0026] Figure 3 It is a structural schematic diagram of the device for determining the meshing stiffness of a helical gear provided by an embodiment of the present invention;

[0027] Figure 4 It is a schematic diagram of the dynamic model of the helical gear transmission;

[0028] Figure 5 Schematic diagram of the contact line and meshing position of the helical gear;

[0029] Figure 6 Calculation model diagram of the load angle of the sliced helical gear;

[0030] Figure 7 Force analysis diagram of the meshing point of the helical gear pair;

[0031] Figure 8 Meshing stiffness calculation result of the helical gear pair. Specific implementation manner

[0032] In the description of the present invention, the terms "first", "second", "third", "fourth", etc. (if any) in the specification and claims of the present invention and the above drawings are used to distinguish similar objects, and do not necessarily need to be used to describe a specific order or sequence. It should be understood that such data used can be interchanged under appropriate circumstances so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "including" or "having" and any deformation thereof are intended to cover non-exclusive inclusion. For example, a process, method, device, product or equipment including a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or equipment.

[0033] For ease of understanding, the following describes the specific process of the embodiments of the present invention. Please refer to Figure 1 , an embodiment of the method for determining the meshing stiffness of a helical gear in the embodiments of the present invention includes:

[0034] 101. Analyze the meshing process of the helical gear based on the obtained design parameters and working conditions parameters of the helical gear to obtain the initial meshing stiffness;

[0035] In this embodiment, the initial meshing stiffness can be first solved according to the gear meshing theory analysis and calculation methods in the prior art (such as the common potential energy method, finite element method, and Ishikawa method);

[0036] Please refer to Table 1. Table 1 shows the design parameters and working conditions parameters of the helical gear pair studied in this embodiment.

[0037] Table 1 Gear design parameters and working conditions parameters

[0038]

[0039] Taking the potential energy method as an example, based on the Hertz contact principle, it quantifies the relationship between the elastic deformation and the load in the gear contact area through the geometric characteristics of the gear contact area (i.e., the module, number of teeth, normal pressure angle, and tooth width in Table 1) and the material characteristics (i.e., the elastic modulus and Poisson's ratio in Table 1), so as to solve the gear mesh stiffness; specifically, it first solves the radius of curvature of the meshing point based on the module, the number of teeth of the driving and driven wheels, and the normal pressure angle, and then substitutes the elastic modulus, Poisson's ratio, radius of curvature, and tooth width into the Hertz contact theory to quantify the relationship between the elastic deformation and the load in the gear contact area, thereby obtaining the calculation of the initial mesh stiffness of the gear pair at a certain moment ; The initial mesh stiffness is the mesh stiffness calculated only based on the gear geometric dimensions and material characteristics under the ideal meshing state without considering the coupling effect of tooth surface friction and meshing, and it is used for the initial input of the subsequent helical gear transmission model.

[0040] 102. Conduct dynamic analysis of the helical gear transmission based on the initial mesh stiffness to obtain the dynamic response;

[0041] In this embodiment, first construct a dynamic model that can accurately describe the characteristics of the helical gear transmission, and then introduce the initial mesh stiffness into the model to form a system of dynamic equations, and obtain the dynamic response of the system under the initial conditions by solving the equations, providing basic data for the further analysis and optimization of the helical gear transmission system.

[0042] 103. Discretize the helical gear pair and determine the coordinate information of the meshing points of each sliced helical gear obtained by the discretization process, and confirm the load angles of each sliced helical gear based on the coordinate information of the meshing points;

[0043] In this embodiment, based on the idea of the "slicing method", discretize the helical gear pair along the tooth width direction, which can reduce the modeling difficulty of the helical gear mesh stiffness, and can accurately determine the coordinate information of the meshing points and the load angles of each sliced helical gear, helping to deeply understand the meshing characteristics of the helical gear pair.

[0044] 104. Analyze the meshing situation of the sliced helical gears under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle to obtain the mesh stiffness of the sliced helical gear pair;

[0045] In this embodiment, first decompose the meshing force and the frictional force based on the preset initial load distribution information and dynamic response, consider the influence of friction on the load distribution, and then calculate the sliced mesh stiffness including the friction effect through the Hertz contact theory and the formula of material mechanics.

[0046] 105. Determine the load distribution information of each slice and each contact line based on the mesh stiffness of the sliced helical gear pair and the initial load distribution information to obtain the corrected mesh stiffness;

[0047] In this embodiment, by considering the interaction between the contact lines and slices in the helical gear pair, the load distribution information is determined, and then the meshing stiffness of the helical gear pair is solved.

[0048] 106. Judge whether the preset convergence condition is satisfied based on the modified meshing stiffness and the initial meshing stiffness, and obtain the convergence judgment result.

[0049] In this embodiment, since the change in load distribution will directly affect the force state of the gear and then change the dynamic response, it is necessary to correct the dynamic response, recalculate the modified meshing stiffness, and form an iterative cycle until the modified meshing stiffness meets the convergence condition.

[0050] 107. If the convergence judgment result is that the convergence condition is satisfied, judge whether the preset iteration stop condition is satisfied. If not, use the modified meshing stiffness as the initial meshing stiffness, and return to perform the dynamic analysis of helical gear transmission based on the initial meshing stiffness.

[0051] In the embodiment of the present invention, the initial meshing stiffness is obtained by analyzing the meshing process based on the design parameters and working condition parameters of the helical gear. Then, based on the initial meshing stiffness, the meshing stiffness of the helical gear is determined to obtain the initial dynamic response. Using the initial dynamic response as the basis, the meshing process of spur gears under tooth surface friction is analyzed. Through iterative calculation, a closed-loop iteration of "stiffness calculation - load distribution - stiffness correction" is realized, so that the model gradually converges on the basis of considering the interaction between dynamic meshing force and friction, approaching the true performance of the helical gear transmission system, thereby providing an accurate basis for determining the meshing stiffness of the helical gear.

[0052] Two embodiments of the method for determining the meshing stiffness of helical gears in the embodiments of the present invention include that step 102 includes:

[0053] 201. Construct a dynamic model of helical gear transmission.

[0054] In the embodiment, referring to Figure 4 , first assume that the driving and driven wheels each have x, y, z, degrees of freedom in the same directions (denoted as , , and , i = p, g, representing the driving and driven wheels respectively); then, based on the principle of lumped mass method, construct a dynamic model of the helical gear transmission system; the dynamic model of the helical gear transmission system simplifies each component in the helical gear system into lumped mass units with certain mass and moment of inertia, and these units are connected to each other through springs and dampers to simulate the meshing stiffness and meshing damping of the gears; in the figure, k and care the meshing stiffness and meshing damping of the helical gear pair, α is the engagement angle, Φ Mounting angle for the driven wheel, is the angle between the meshing line of the helical gear pair and the y-axis; and are the torque and speed transmitted by gear i respectively.

[0055] 202. The initial meshing stiffness is introduced into the helical gear transmission dynamics model to obtain the helical gear transmission dynamics equations;

[0056] In this embodiment, after the helical gear transmission dynamics model is constructed, the helical gear transmission dynamics equations can be obtained according to the force conditions of the components of the helical gear transmission system and Newton's second law;

[0057] (1)

[0058] Where, X=[ x p , y p , z p , θ p , x g , y g , z g , θ g ]′、M、 and They are the system degree of freedom matrix, mass matrix, error excitation matrix and external load matrix respectively; is the second-order derivative of X; It can be determined by the design parameters and working parameters of the helical gear, M and It can be obtained from formula (2)-formula (3):

[0059] (2)

[0060] (3)

[0061] Where, k is the meshing stiffness (i.e. the initial meshing stiffness Or modify the meshing stiffness ); and are the mass and polar moment of inertia of gear i, 、 、 is the bearing support force borne by gear i in the x, y, and z directions; and The torque and base circle radius respectively transmitted by (i = p, g) The dynamic transmission error of the helical gear pair can be obtained by the following formula:

[0062] (4)

[0063] In formula (4), 、 and are the displacements of gear i in the x, z and directions, and β is the helix angle of the helical gear;

[0064] The dynamic transmission error of the helical gear pair obtained based on formula (4) , the dynamic meshing force of the helical gear pair F mesh can be obtained by the following formula:

[0065] (5)

[0066] In formula (5), k and c are respectively the meshing stiffness and meshing damping of the helical gear pair, is the dynamic transmission error speed of the helical gear pair;

[0067] The dynamic equations of helical gear transmission are used to describe the motion and force relationship of the helical gear transmission system. By solving the equations numerically, the dynamic response parameters such as the force and displacement of the gear can be obtained.

[0068] 203. Solve the dynamic equations of helical gear transmission to obtain the initial dynamic response;

[0069] In this embodiment, the above equations are solved by a numerical solution method (such as the Runge - Kutta method) to obtain the initial dynamic response, and the initial dynamic response includes dynamic parameters such as the force and displacement of the helical gear;

[0070] The initial dynamic response can understand the basic dynamic characteristics of the system when the coupling effect between tooth surface friction and meshing is not considered. On this basis, further analyzing the helical gear transmission system can accurately evaluate the influence of tooth surface friction on the meshing process of the helical gear.

[0071] In the three embodiments of the method for determining the meshing stiffness of helical gears in the embodiments of the present invention, step 103 includes:

[0072] 301. Discretize the helical gear pair along the tooth width direction to obtain a plurality of sliced helical gears;

[0073] In this embodiment, since there are multiple contact lines on the helical gear and any point on the contact line participates in meshing, the discretization process can transform the complex helical gear meshing problem into multiple simple meshing problems of sliced helical gear pairs;

[0074] Referring to Figure 5 , according to the idea of the "slicing method", taking the driving wheel as an example, the helical gear is discretized along the tooth width direction; the slices are evenly distributed along the tooth width direction. Let the tooth width of the sliced helical gear be , the number of slices be n, and the tooth width of the helical gear be B, then = B / n; each contact line is parallel to each other in the meshing plane and separated by a base circular pitch ; and are the intersection points of the meshing line of the helical gear pair and the addendum circles of the driving and driven wheels respectively, is the length of the meshing plane; <( and are the corresponding points that are separated from and by the tooth width B. This uniform discretization method can make each slice have similar characteristics in subsequent analysis, facilitating unified processing.

[0075] 302. Construct a local coordinate system to determine the meshing positions of the discretized sliced helical gear pairs;

[0076] In this embodiment, referring to Figure 5 , after the discretization is completed, in order to accurately describe the positions and motion states of the sliced helical gears, we need to construct a suitable coordinate system. By establishing the local coordinate system , we can represent the positions of the sliced helical gears in the form of coordinates; in the figure, the meshing points of each sliced helical gear pair are the intersection points of the slice center line and the contact line; project the point X onto the meshing line , and the meshing position of the sliced helical gear pair on the meshing line can be determined by the projection point . According to the gear meshing principle, is the projection meshing position of the sliced helical gear pair corresponding to the point on the end face of the helical gear pair. By determining the position of the projection point , we can more intuitively understand the meshing situation of the sliced helical gear pair on the end face, and thus determine the meshing parameters of the sliced helical gear pair at the point, such as the meshing position, pressure angle, contact line length, etc.

[0077] 303. Analyze the force direction of the helical gear pair based on the meshing position of each sliced helical gear to obtain the load angle of each sliced helical gear;

[0078] In this embodiment, the load angle is the angle between the normal direction of the tooth surface and the circumferential tangential direction at the meshing point X, reflecting the influence of the load action direction on the meshing stiffness; The calculation model of the load angle of the sliced helical gear is as Figure 6 shown; In the figure, X is the meshing point, H is the tooth tip, L is the midpoint of the tooth tip, is the tooth center distance from the meshing point X to the tooth center of the driving wheel, is the line of action, is the base circle radius of the driving wheel, is the pressure angle at the meshing point, is the load angle at the meshing point, and point M is the foot of the perpendicular from X to the tooth center line O p L ;

[0079] According to the geometric parameters of the driving wheel, the load angle is determined by Equation (6):

[0080] (6)

[0081] In Equation (6), is the number of teeth of the driving wheel, inv() is the involute function, and are the pressure angles of the driving wheel at the meshing point X and the pitch circle respectively. The sign is determined by the relationship between the tooth center distance at the meshing point and the pitch circle radius : If < , Equation (6) takes the + sign; if ≥ , Equation (5) takes the - sign; The tooth center distance at the meshing point can be calculated based on the meshing position;

[0082] Similarly, the load angle of the driven wheel slice is calculated through symmetric geometric relationships to ensure the consistency of the load directions at the meshing points of the driving and driven wheels.

[0083] In the four embodiments of the method for determining the meshing stiffness of helical gears in the embodiments of the present invention, step 104 includes:

[0084] 401. Analyze the force conditions of the sliced helical gears under tooth surface friction based on the preset initial load distribution information and dynamic response to obtain the frictional force and meshing force of each sliced helical gear;

[0085] The dynamic response is used to reflect the overall force state of the helical gear transmission system; taking the slice of the driving gear as an example, the dynamic meshing force output by the dynamic model F mesh is input as the total load;

[0086] First, a calculation model for the meshing stiffness of the helical gear pair considering tooth surface friction is constructed, referring to Figure 7 ; then it is assumed that the load is evenly distributed on each contact line and each slice of the helical gear (i.e., the preset initial load distribution information), and the meshing force F mesh is substituted into Equation (22), and the load allocated to the mth slice of the helical gear pair on the kth contact line can be obtained according to Equation (22) and Equation (21) F m，kk (k = 1, 2, …, N, m = 1, 2, …, n, where N and n are the number of contact lines and the number of slices respectively); then F m，kk is decomposed into the tangential component and the radial component ;

[0087] Their expressions are as follows:

[0088] (7)

[0089] (8)

[0090] In the formula, is the normal pressure angle, is the helix angle.

[0091] Assume that the tooth surface friction satisfies Coulomb's law, that is, the frictional force = ( is the friction coefficient), then the tangential component and the radial component of its frictional force can be obtained, and their expressions are as follows:

[0092] (9)

[0093] (10)

[0094] (11)

[0095] From Figure 7 it can be seen that the directions of the tangential component and the radial component are related to the position of the meshing point and the pitch line. For the convenience of subsequent derivation, the resultant force and , as shown in Equations (12) and (13):

[0096] (12)

[0097] (13)

[0098] In Equations (12) and (13), when the meshing position is below the pitch line, the upper symbol is selected; conversely, the lower symbol is selected; see Figure 7 , the intersection point of the common normal of the tooth profile contact point and the line of centers is called the pitch point, and the locus of the pitch point on the gear during the meshing process of a pair of tooth profiles is called the pitch line.

[0099] 402. Analyze the meshing condition of the sliced helical gear based on the load angle, frictional force, and meshing force of each sliced helical gear to obtain the meshing stiffness of the sliced helical gear pair;

[0100] According to the energy method, during the meshing process, the potential energy stored in the meshing teeth of the driving and driven wheels includes four parts: Hertz contact potential energy, bending potential energy, radial compression potential energy, and shear potential energy; these four parts of potential energy correspond to the Hertz contact stiffness k h,m,kk , bending stiffness k bi,m,kk , radial compression stiffness k ai,m,kk and shear stiffness k si,m,kk , which can be obtained from the mechanics of materials:

[0101] (14)<e

[0102] (15)

[0103] (16)

[0104] (17)

[0105] In the formula, B is the tooth width of the helical gear, , and are the elastic modulus, shear modulus, and Poisson's ratio of gear i, respectively, b m，kk and are the Hertz contact half-width and radius of curvature of gear i at the meshing point X, respectively; d is the vertical distance from the meshing point X to the root circle, h is the tooth thickness at the meshing point X, x, and are the vertical distance from the infinitesimal dx to the root circle, the cross-sectional area at the infinitesimal dx, and the polar moment of inertia, respectively; among them, d and h are related to the load angle at the meshing point X parameters directly related to (i = p, g), Hertzian contact half-width b m，kk and the load F m，kk parameters directly related; b m，kk related to F m，kk The relationship with is shown in Equation (18);

[0106] (18)

[0107] Therefore, the tooth body meshing stiffness of the sliced helical gear pair k tt,m,kk (kk = 1, 2, …, N, m = 1, 2, …, n, N and n are the number of contact lines and the number of slices respectively) is shown in Equation (19):

[0108] (19)

[0109] In addition, during the gear meshing process, the gear matrix will also undergo a certain deformation, and the stiffness corresponding to this part of the deformation is the matrix stiffness ;

[0110] In summary, the meshing stiffness of the sliced helical gear pair can be obtained from Equation (20):

[0111] (20)

[0112] In the formula, (i = p, g) is the matrix deformation correction coefficient of gear i, generally 1.1; (i = p, g) is the matrix stiffness of gear i.

[0113] In the five embodiments of the method for determining the meshing stiffness of helical gears in the embodiments of the present invention, step 105 includes:

[0114] 501. Based on the meshing stiffness of the sliced helical gear pair and the initial load distribution information, determine the load distribution information of each slice and each contact line to obtain the contact line load distribution information and the meshing stiffness of the contact line helical gear pair;

[0115] As can be seen from Equation (14), the Hertzian contact stiffness of the sliced helical gear pair is related to the load it bears, which indicates that the load borne by the slice will affect its contact stiffness, and the contact stiffness is closely related to the meshing condition of the slice; therefore, by establishing a slice load distribution equation, the slice load distribution information between slices on a certain contact line can be determined;

[0116] The slice m bears the load (where \(k = 1, 2, \cdots, N\), \(m = 1, 2, \cdots, n\), \(N\) and \(n\) are the number of contact lines and the number of slices respectively) and the meshing stiffness of the contact line helical gear pair can be obtained from the slice load distribution equation, as shown in Equation (21):

[0117] (21)

[0118] In the formula, is the load borne by slice \(m\) in contact line \(k\), are respectively the meshing errors borne by slice \(m\) in contact line \(k\), 、 and are respectively the load, meshing stiffness and meshing error borne by contact line \(k\);

[0119] Since the meshing loads distributed to each contact line of the helical gear pair are not independent but need to satisfy a certain coordination relationship, therefore, a load coordination equation needs to be established to determine the load distribution relationship between each contact line, so as to obtain the contact line load distribution information;

[0120] The load of contact line \(k\) and the numbers of the contact lines participating in meshing can be determined by the load coordination equation, as shown in Equation (22):

[0121] (22)

[0122] In the formula, \(N\) is the number of contact lines of the helical gear pair, is the dynamic meshing force of the helical gear pair;

[0123] In this embodiment, based on the initial load distribution information, it can be assumed that the load is evenly distributed on each contact line and each slice of the helical gear. Then, according to Equation (20), the meshing stiffness of the slice helical gear pair and the meshing errors of each slice helical gear pair can be obtained, and the meshing stiffness of contact line \(k\) and the meshing error can be obtained; substituting this assumed value into Equation (22), the load of contact line \(k\) can be obtained by using the dynamic meshing force of the helical gear pair determined by Equation (1);

[0124] Substituting the assumed value of the load of contact line \(k\) into Equation (21), the meshing forces of each slice helical gear pair can be obtained; at this time, if the obtained < 0, it indicates that on the kk th contact line, the mOne slice of the helical gear pair is not engaged, that is, the corresponding parameters are removed from the load distribution equation of this slice, so as to know the slices actually engaged on the contact line kk;

[0125] After knowing the slices actually engaged on the contact line kk, the meshing stiffness of the slice helical gear pair can be reused to calculate the meshing stiffness of the contact line kk , and then substitute it back into Equation (22) to obtain the load of the contact line kk ; At this time, if the obtained F kk <0, it indicates that the kk th contact line is not engaged, that is, the corresponding parameters are removed from this load coordination equation, so as to know the number of the contact line participating in the engagement;

[0126] Repeat the above steps, gradually eliminate the slices and contact lines that do not participate in the engagement, and finally determine the slices and contact lines actually participating in the engagement and their corresponding load distributions. At this time, the meshing stiffness of the contact line kk participating in the engagement can be obtained (i.e., the meshing stiffness of the contact line helical gear pair) and the number of the contact line participating in the engagement (i.e., the load distribution information of the contact line).

[0127] 502. Based on the load distribution information of the contact line, perform superposition calculation on the meshing stiffness of the contact line helical gear pair to obtain the corrected meshing stiffness;

[0128] After obtaining the meshing stiffness of each contact line helical gear pair and the load distribution information between each contact line, it is necessary to superpose the meshing stiffness of the contact line helical gear pairs participating in the engagement to obtain the meshing stiffness of the helical gear pair;

[0129] (23)

[0130] In the formula, is the set of the numbers of the contact lines in which the helical gear pair participates in the engagement determined according to Equation (22);

[0131] In this embodiment, as shown in Equation (23), after obtaining the meshing stiffness of the contact line helical gear pair, superpose it along the tooth width direction, and the meshing stiffness of the helical gear pair considering the tooth surface friction, that is, the corrected meshing stiffness, can be obtained .

[0132] In the six embodiments of the method for determining the meshing stiffness of helical gears in the embodiments of the present invention, after step 106, it further includes:

[0133] 601. If the convergence judgment result does not meet the convergence condition, use the load distribution information as the preset initial load distribution information, and return to execute the analysis of the meshing situation of the slice helical gear under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle;

[0134] In this embodiment, it is determined whether the current corrected meshing stiffness meets the convergence condition through Equation (24).

[0135] (24)

[0136] In the formula, abs is the absolute value function. When it is not satisfied it indicates that the current meshing stiffness has not converged. At this time, the load distribution information of each slice and the contact line obtained in step 501 (that is, the number of the contact line finally participating in meshing and the number of the slice helical gear pair) is used to replace the preset initial load distribution information, and then the meshing force F mesh is substituted into Equation (22). According to Equation (22) and Equation (21), the load allocated to the slice helical gear pair can be calculated F m，kk , and F m，kk is used to re-solve the Hertz contact half-width b m，kk ; using the newly obtained F m，kk and b m，kk , repeating the above calculation process of the corrected meshing stiffness, the new corrected meshing stiffness can be obtained; repeating this iterative correction process until the obtained corrected meshing stiffness meets the convergence condition.

[0137] In the seven embodiments of the method for determining the meshing stiffness of helical gears in the embodiments of the present invention, step 107 includes:

[0138] 701. If the current iteration time < the preset maximum iteration time, the preset iteration stop condition is not satisfied;

[0139] In this embodiment, the upper limit of the simulation time is set according to engineering requirements. After each iteration, the system reads the current simulation time and compares it with the upper limit of the simulation time . If < , the iteration loop is triggered.

[0140] 702. Use the corrected meshing stiffness as the initial meshing stiffness, and return to perform the dynamic analysis of helical gear transmission based on the initial meshing stiffness to obtain the dynamic response;

[0141] In this embodiment, the corrected meshing stiffness is the optimization result of the current iteration and is more in line with the actual meshing characteristics. The corrected meshing stiffness obtained through iteration is re-input into the helical gear transmission system for analysis, enabling the determination of the helical gear meshing stiffness to be continuously optimized and improved. As the number of iterations increases, the analysis results will gradually approach the true performance of the system, thereby providing a more accurate basis for determining the helical gear meshing stiffness.

[0142] Please refer to Figure 8 , and it can be seen from Figure 8 that there is a large difference between the meshing stiffness obtained by the method of the present invention and the value calculated by the energy method. This is because the dynamic meshing excitation caused by the tooth surface friction and gear meshing coupling of the helical gear pair will change the load distribution situation between the meshing points of the helical gear pair, thereby affecting the meshing of the gear pair. This phenomenon indicates that the coupling effect between the tooth surface friction and gear meshing of the helical gear pair has a significant impact on the meshing mechanism and even the dynamic response of the helical gear.

[0143] The method for determining the helical gear meshing stiffness in the embodiment of the present invention has been described above. Next, the device for determining the helical gear meshing stiffness in the embodiment of the present invention will be described. Please refer to Figure 2 , and an embodiment of the device for determining the helical gear meshing stiffness in the embodiment of the present invention includes:

[0144] An initialization module 801, configured to analyze the meshing process of the helical gear based on the obtained design parameters and working condition parameters of the helical gear to obtain an initial meshing stiffness;

[0145] A transmission analysis module 802, configured to perform helical gear transmission dynamics analysis based on the initial meshing stiffness to obtain a dynamic response;

[0146] A discretization module 803, configured to perform discretization processing on the helical gear pair, determine the meshing point coordinate information of each sliced helical gear obtained by the discretization processing, and confirm the load angle of each sliced helical gear based on the meshing point coordinate information;

[0147] A first calculation module 804, configured to analyze the meshing situation of the sliced helical gear under tooth surface friction based on the dynamic response and the load angle to obtain the meshing stiffness of the sliced helical gear pair;

[0148] A second calculation module 805, configured to determine the load distribution information of each slice and each contact line based on the meshing stiffness of the sliced helical gear pair and the initial load distribution information to obtain a corrected meshing stiffness;

[0149] A judgment module 806, configured to judge whether a preset convergence condition is satisfied based on the corrected meshing stiffness and the initial meshing stiffness to obtain a convergence judgment result;

[0150] The iterative module 807 is configured to determine whether a preset iteration stop condition is satisfied if the convergence judgment result shows that the convergence condition is satisfied. If not, the modified meshing stiffness is used as the initial meshing stiffness, and the process returns to execute the model solution by introducing the helical gear transmission dynamics model based on the initial meshing stiffness.

[0151] In this embodiment, the initialization module 801 first analyzes the meshing process based on the design parameters and operating parameters of the helical gear to obtain the initial meshing stiffness, and then the transmission analysis module 802 performs transmission analysis based on the initial meshing stiffness to obtain the initial dynamic response; the discretization module 803, the first calculation module 804 and the second calculation module 805 use the initial dynamic response as the basis to analyze the meshing process of the spur gear under tooth surface friction, and implement the closed-loop iteration of "stiffness calculation-load distribution-stiffness correction" through the judgment module 806 and the iteration module 807, so that the model gradually converges on the basis of considering the interaction between dynamic meshing force and friction, and approaches the actual performance of the helical gear transmission system, thereby providing a basis for determining the meshing stiffness of the helical gear.

[0152] Figure 3 FIG2 is a schematic diagram of the structure of a device for determining helical gear mesh stiffness provided by an embodiment of the present invention. The device 900 may vary significantly depending on configuration or performance. The device may include one or more central processing units (CPUs) 910 (e.g., one or more processors), a memory 920, and one or more storage media 930 (e.g., one or more mass storage devices) storing application programs 933 or data 932. The memory 920 and storage medium 930 may be either transient or persistent storage. The program stored in the storage medium 930 may include one or more modules (not shown), each of which may include a series of instructions for operating on the device 900. Furthermore, the processor 910 may be configured to communicate with the storage medium 930, allowing the device 900 to execute the series of instructions stored in the storage medium 930 to implement the steps of the helical gear mesh stiffness determination method provided in the aforementioned method embodiments.

[0153] The helical gear meshing stiffness determination device 900 may further include one or more power supplies 940, one or more wired or wireless network interfaces 950, one or more input and output interfaces 960, and / or one or more operating systems 931, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. It will be understood by those skilled in the art that Figure 3The shown structure of the helical gear meshing stiffness determination device does not constitute a limitation on the helical gear meshing stiffness determination device, and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0154] The present invention also provides a computer-readable storage medium. The computer-readable storage medium can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium. Instructions are stored in the computer-readable storage medium. When the instructions run on a computer, the computer is caused to execute the steps of the helical gear meshing stiffness determination method.

[0155] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the above-described device or devices and units can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0156] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM), random access memories (RAM), magnetic disks, or optical discs that can store program codes.

[0157] Finally, it should be noted that the above are only preferred examples of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for determining the meshing stiffness of helical gears, characterized in that Including: Analyze the meshing process of the helical gear pair based on the obtained design parameters and working conditions of the helical gear pair to obtain the initial meshing stiffness; Conduct dynamic analysis of helical gear transmission based on the initial meshing stiffness to obtain the dynamic response; Discretize the helical gear and determine the meshing point coordinate information of each sliced helical gear obtained by the discretization process. Based on the meshing point coordinate information, confirm the load angles of each sliced helical gear; Analyze the meshing condition of the sliced helical gear pair under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle to obtain the meshing stiffness of the sliced helical gear pair; Based on the meshing stiffness of the sliced helical gear pair and the initial load distribution information, determine the load distribution information of each slice and each contact line to obtain the modified meshing stiffness; Judge whether the preset convergence condition is satisfied based on the modified meshing stiffness and the initial meshing stiffness to obtain the convergence judgment result; If the convergence judgment result is that the convergence condition is satisfied, then judge whether the preset iteration stop condition is satisfied. If not, use the modified meshing stiffness as the initial meshing stiffness and return to execute the step of conducting dynamic analysis of helical gear transmission based on the initial meshing stiffness; The analyzing the meshing condition of the sliced helical gear pair under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle to obtain the meshing stiffness of the sliced helical gear pair includes: Analyzing the force condition of the sliced helical gear under tooth surface friction based on the preset initial load distribution information and dynamic response to obtain the friction force and meshing force of each sliced helical gear; Analyzing the meshing condition of the sliced helical gear pair based on the load angle, friction force, and meshing force of each sliced helical gear to obtain the meshing stiffness of the sliced helical gear pair; Among them, the Hertz contact stiffness of the sliced helical gear pair can be analyzed first according to the load angle, frictional force, and meshing force of each sliced helical gear k h,m,kk , bending stiffness k bi,m,kk , radial compression stiffness k ai,m,kk and shear stiffness k si,m,kk , and then the meshing stiffness of the sliced helical gear pair can be obtained; the expressions of the Hertz contact stiffness k h,m,kk , bending stiffness k bi,m,kk , radial compression stiffness k ai,m,kk and shear stiffness k si,m,kk are as follows: ； ； ； ； In the formula, gear \(i\) is denoted as \(p\) or \(g\), representing the driving gear and the driven gear respectively; \(B\) is the tooth width of the helical gear; 、 and are the elastic modulus, shear modulus and Poisson's ratio of gear \(i\) respectively; b m，kk and are the Hertz contact half-width and the radius of curvature of gear \(i\) at the meshing point \(X\) respectively; \(d\) is the vertical distance between the meshing point \(X\) and the root circle; \(h\) is the tooth thickness at the meshing point \(X\); \(x\), and are the vertical distance between the infinitesimal \(dx\) and the root circle, the cross-sectional area and the polar moment of inertia at the infinitesimal \(dx\) respectively; and are the resultant forces of the helical gear in the radial and tangential directions; F m，kk is the load assigned to the \(m\)th slice helical gear pair on the \(k\)th contact line.

2. The method for determining the meshing stiffness of helical gears according to claim 1, characterized in that, The conducting dynamic analysis of helical gear transmission based on the initial meshing stiffness to obtain the dynamic response includes: Construct a dynamic model of helical gear transmission; Introduce the initial meshing stiffness into the dynamic model of helical gear transmission to obtain a dynamic equation set of helical gear transmission; Solve the dynamic equation set of helical gear transmission to obtain the initial dynamic response.

3. The method for determining the helical gear meshing stiffness according to claim 1, wherein The discretizing the helical gear and determining the meshing point coordinate information of each sliced helical gear obtained by the discretization process. Based on the meshing point coordinate information, confirm the load angles of each sliced helical gear includes: Discretize the helical gear along the tooth width direction to obtain multiple sliced helical gears; Construct a local coordinate system to determine the meshing positions of each sliced helical gear obtained by the discretization process; Analyze the force direction of the helical gear based on the meshing positions of each sliced helical gear to obtain the load angles of each sliced helical gear.

4. The method for determining the helical gear meshing stiffness according to claim 1, characterized in that The based on the meshing stiffness of the sliced helical gear pair and the initial load distribution information, determining the load distribution information of each slice and each contact line to obtain the modified meshing stiffness includes: Based on the meshing stiffness of the sliced helical gear pair and the initial load distribution information, determine the load distribution information of each slice and each contact line to obtain the contact line load distribution information and the meshing stiffness of the contact line helical gear pair; Conduct superposition calculation on the meshing stiffness of the contact line helical gear pair based on the contact line load distribution information to obtain the modified meshing stiffness.

5. The method for determining the meshing stiffness of helical gears according to claim 1, characterized in that, After determining whether the preset convergence condition is satisfied based on the corrected meshing stiffness and the initial meshing stiffness and obtaining the convergence judgment result, the following steps are further included: If the convergence judgment result indicates that the convergence condition is not satisfied, the load distribution information is used as the preset initial load distribution information, and the step of analyzing the meshing condition of the sliced helical gear pair under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle is returned for execution.

6. The method for determining the helical gear meshing stiffness according to claim 1, wherein If the convergence judgment result indicates that the convergence condition is satisfied, it is determined whether the preset iteration stop condition is satisfied. If not, the corrected meshing stiffness is used as the initial meshing stiffness, and the step of performing dynamic analysis of helical gear transmission based on the initial meshing stiffness is returned for execution, including: If the current iteration time < the preset maximum iteration time, the preset iteration stop condition is not satisfied; The corrected meshing stiffness is used as the initial meshing stiffness, and the step of performing dynamic analysis of helical gear transmission based on the initial meshing stiffness is returned for execution.

7. A helical gear meshing stiffness determination device, characterized in that Including: An initialization module for analyzing the meshing process of the helical gear pair based on the obtained design parameters and working condition parameters of the helical gear pair to obtain the initial meshing stiffness; A transmission analysis module for performing dynamic analysis of helical gear transmission based on the initial meshing stiffness to obtain the dynamic response; A discretization module for discretizing the helical gear and determining the meshing point coordinate information of each sliced helical gear obtained by the discretization process, and confirming the load angle of each sliced helical gear based on the meshing point coordinate information; A first calculation module for analyzing the meshing condition of the sliced helical gear pair under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle to obtain the meshing stiffness of the sliced helical gear pair; Analyzing the meshing condition of the sliced helical gear pair under tooth surface friction based on the preset initial load distribution information, dynamic response, and load angle to obtain the meshing stiffness of the sliced helical gear pair includes: analyzing the force condition of the sliced helical gear under tooth surface friction based on the preset initial load distribution information and dynamic response to obtain the frictional force and meshing force of each sliced helical gear; analyzing the meshing condition of the sliced helical gear pair based on the load angle, frictional force, and meshing force of each sliced helical gear to obtain the meshing stiffness of the sliced helical gear pair; Among them, the Hertz contact stiffness of the sliced helical gear pair can be analyzed first according to the load angle, frictional force, and meshing force of each sliced helical gear k h,m,kk , bending stiffness k bi,m,kk , radial compression stiffness k ai,m,kk and shear stiffness k si,m,kk , and then the meshing stiffness of the sliced helical gear pair can be obtained; Hertz contact stiffness k h,m,kk , flexural stiffness k bi,m,kk , radial compression stiffness k ai,m,kk and shear stiffness k si,m,kk are expressed as follows: ； ； ； ； In the formula, gear i is denoted as p or g, representing the driving gear and the driven gear respectively; B is the tooth width of the helical gear; 、 and are the elastic modulus, shear modulus and Poisson's ratio of gear i respectively; b m，kk and are the Hertzian contact half-width and the radius of curvature at the meshing point X of gear i respectively; d is the perpendicular distance from the meshing point X to the root circle; h is the tooth thickness at the meshing point X; x, and are the perpendicular distance from the infinitesimal dx to the root circle, the cross-sectional area and the polar moment of inertia at the infinitesimal dx respectively; and are the resultant forces of the helical gear in the radial and tangential directions; F m，kk is the load assigned to the m-th slice helical gear pair on the k-th contact line; A second calculation module for determining the load distribution information of each slice and each contact line based on the meshing stiffness of the sliced helical gear pair and the initial load distribution information to obtain the corrected meshing stiffness; A judgment module for determining whether the preset convergence condition is satisfied based on the corrected meshing stiffness and the initial meshing stiffness to obtain the convergence judgment result; An iteration module for, if the convergence judgment result indicates that the convergence condition is satisfied, determining whether the preset iteration stop condition is satisfied. If not, using the corrected meshing stiffness as the initial meshing stiffness and returning to the transmission analysis module.

8. An equipment for determining the meshing stiffness of helical gears, characterized in that, The helical gear meshing stiffness determination device includes: a memory and at least one processor, and instructions are stored in the memory; At least one of the processors calls the instructions in the memory so that the helical gear meshing stiffness determination device executes each step of the helical gear meshing stiffness determination method according to any one of claims 1-6.

9. A computer-readable storage medium having instructions stored thereon, characterized in that, When the instruction is executed by a processor, each step of the helical gear meshing stiffness determination method according to any one of claims 1-6 is implemented.

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